In this paper, we study locally strongly convex affine hypersurfaces with vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of metric. As main result, classify such being not flat particular, $2, 3$-dimensional are completely determined.

We undertake the construction of quadratic parity-violating terms involving curvature in four-dimensional metric-affine gravity. demonstrate that there are only 12 linearly independent scalars, plus an additional one can be removed by using Pontryagin invariant. Several convenient bases for this sector provided both components and differential form notation. also particularize our general findi...

This paper presents the detailed, standard treatment of a simple, gauge invariant action for Weyl and Weyl-like Cartan geometries outlined in a previous paper. In addition to the familiar scalar curvature squared and Maxwell terms, the action chosen contains the logarithmic derivative of the scalar curvature combined with the intrinsic four vector (Weyl vector) in a gauge invariant fashion. Thi...

Causal structure, inertial path structure and compatibility with quantum mechanics demand no full Lorentz metric, but only an integrable Weyl geometry for space time (Ehlers/Pirani/Schild 1972, Audretsch e.a. 1984). A proposal of (Tann 1998, Drechsler/Tann 1999) for a minimal coupling of the Hilbert-Einstein action to a scale covariant scalar vacuum field φ (weight −1) plus (among others) a Kle...

We introduce the concept of quasi-semi-Weyl structure, we provide a couple ways for constructing quasi-statistical and structures by means pseudo-Riemannian metric, an affine connection tensor field on smooth manifold, place these in relation with one another.

‎in this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular sturm-liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎also weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

We briefly review the basics of Weyl geometry and its natural extension by a general linear ”distortion” of the metric connection by a vector field. A special class of the connections has torsion but retains the Weyl’s semi-metricity condition. We present ghost-free gravitational theories in this geometrical setup and highlight their possible cosmological applications, such as new self-tuning s...

The response of the one loop effective action for a gauge theory with local couplings g(x), θ(x) under a local Weyl rescaling of the background metric is calculated. Apart from terms which may be removed by local contributions to the effective action the result is compatible with Sl(2, R) symmetry acting on g, θ. Two loop effects are also discussed. PACS no:11.10Gh, 11.15-q, 11.30Pb

We study in detail the static spherically symmetric vacuum solution to conformal (Weyl) gravity. One of the more striking aspects of the solution is the presence of a physical singularity at r = 0 due to the linear term in the metric. Using Penrose diagrams we determine which conformally flat space-times allow light to scatter from infinity and calculate the trajectories and deflection of light...

Strings propagating in AdSD+1 are made Weyl invariant to leading order in large D by a ghost-matter coupling that preserves the Poincaré symmetry of the boundary. It has been proposed [1] [2] that Wilson loops for gauge theories in flat space with coordinates X i are described by strings in a target space with metric of the form ds = dφ + z(φ) D